For the regression model y = M(x) + ε, adaptive stochastic approximation schemes of the form xn+1 = xn — yn/(nbn) for choosing the levels x1,x2,... at which y1,y2,... are observed converge with probability 1 to the unknown root θ of the regression function M(x). Certain local convergence theorems that relate the convergence rate of xn — θ to the limiting behavior of the random variables bn are established.
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